Copyright	(c) 2014 Patrick Bahr Emil Axelsson
License	BSD3
Maintainer	Patrick Bahr <paba@di.ku.dk>
Stability	experimental
Portability	non-portable (GHC Extensions)
Safe Haskell	None
Language	Haskell98

Data.Comp.PAG

Description

This module implements recursion schemes derived from attribute grammars. The variant implemented in this module, called parametric attribute grammars, generalises both attribute grammars and attribute grammars with rewrite function (as implemented in Data.Comp.AG).

Synopsis

runPAG :: forall f u d g. (Traversable f, Functor g, Functor d, Functor u) => Syn' f (u :*: d) u g -> Inh' f (u :*: d) d g -> (forall a. u a -> d (Context g a)) -> Term f -> u (Term g)
class (Functor t, Foldable t) => Traversable (t :: * -> *)
pr :: p :< q => q a -> p a
type (:<) (f :: * -> *) (g :: * -> *) = Proj (ComprEmb (Elem f g)) f g
fsnd :: (f :*: g) a -> g a
ffst :: (f :*: g) a -> f a
data ((f :: k -> *) :*: (g :: k -> *)) (a :: k) :: forall k. (k -> *) -> (k -> *) -> k -> * = (f a) :*: (g a)
lookupNumMap' :: Int -> NumMap t a -> Maybe a
lookupNumMap :: a -> Int -> NumMap t a -> a
prodMap :: Mapping m k => v1 -> v2 -> m v1 -> m v2 -> m (v1, v2)
number :: Traversable f => f a -> f (Numbered a)
unNumbered :: Numbered a -> a
data Numbered a = Numbered Int a
class Functor m => Mapping (m :: * -> *) k | m -> k where
data NumMap k v
type Inh f p q g = q :< p => Inh' f p q g
type Inh' f p q g = forall m i a. (Mapping m i, ?below :: i -> p a, ?above :: p a) => f i -> m (q (Context g a))
type Syn f p q g = q :< p => Syn' f p q g
type Syn' f p q g = forall child a. (?below :: child -> p a, ?above :: p a) => f child -> q (Context g a)
below :: (?below :: child -> q a, p :< q) => child -> p a
above :: (?above :: q a, p :< q) => p a
prodSyn :: (p :< c, q :< c) => Syn f c p g -> Syn f c q g -> Syn f c (p :*: q) g
(|*|) :: (p :< c, q :< c) => Syn f c p g -> Syn f c q g -> Syn f c (p :*: q) g
prodInh :: (p :< c, q :< c, Functor p, Functor q) => Inh f c p g -> Inh f c q g -> Inh f c (p :*: q) g
(>*<) :: (p :< c, q :< c, Functor p, Functor q) => Inh f c p g -> Inh f c q g -> Inh f c (p :*: q) g

Documentation

runPAG Source #

Arguments

:: (Traversable f, Functor g, Functor d, Functor u)
=> Syn' f (u :*: d) u g	semantic function of synthesised attributes
-> Inh' f (u :*: d) d g	semantic function of inherited attributes
-> (forall a. u a -> d (Context g a))	initialisation of inherited attributes
-> Term f	input term
-> u (Term g)

This function runs a parametric attribute grammar on a term. The result is the (combined) synthesised attribute at the root of the term.

class (Functor t, Foldable t) => Traversable (t :: * -> *) #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality: t . traverse f = traverse (t . f) for every applicative transformation t
identity: traverse Identity = Identity
composition: traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality: t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity: sequenceA . fmap Identity = Identity
composition: sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

```
t (pure x) = pure x
```
```
t (x <*> y) = t x <*> t y
```

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Minimal complete definition

traverse | sequenceA

Instances

Traversable []	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] # sequenceA :: Applicative f => [f a] -> f [a] # mapM :: Monad m => (a -> m b) -> [a] -> m [b] # sequence :: Monad m => [m a] -> m [a] #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Par1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) # sequence :: Monad m => Par1 (m a) -> m (Par1 a) #
Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) # sequence :: Monad m => ZipList (m a) -> m (ZipList a) #
Traversable Identity
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Traversable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #
Traversable Tree
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) # sequence :: Monad m => Tree (m a) -> m (Tree a) #
Traversable IntMap
Instance details Defined in Data.IntMap.Internal Methods traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) # sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) # mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) # sequence :: Monad m => IntMap (m a) -> m (IntMap a) #
Traversable Seq
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
Traversable FingerTree
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) #
Traversable Digit
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b) # sequenceA :: Applicative f => Digit (f a) -> f (Digit a) # mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b) # sequence :: Monad m => Digit (m a) -> m (Digit a) #
Traversable Node
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b) # sequenceA :: Applicative f => Node (f a) -> f (Node a) # mapM :: Monad m => (a -> m b) -> Node a -> m (Node b) # sequence :: Monad m => Node (m a) -> m (Node a) #
Traversable Elem
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b) # sequenceA :: Applicative f => Elem (f a) -> f (Elem a) # mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b) # sequence :: Monad m => Elem (m a) -> m (Elem a) #
Traversable ViewL
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) # sequence :: Monad m => ViewL (m a) -> m (ViewL a) #
Traversable ViewR
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) # sequence :: Monad m => ViewR (m a) -> m (ViewR a) #
Traversable Array
Instance details Defined in Data.Primitive.Array Methods traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) # sequenceA :: Applicative f => Array (f a) -> f (Array a) # mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) # sequence :: Monad m => Array (m a) -> m (Array a) #
Traversable Vector
Instance details Defined in Data.Vector Methods traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) # sequenceA :: Applicative f => Vector (f a) -> f (Vector a) # mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) # sequence :: Monad m => Vector (m a) -> m (Vector a) #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Traversable (V1 :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable (U1 :: * -> *)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Traversable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) # sequence :: Monad m => (a, m a0) -> m (a, a0) #
Ix i => Traversable (Array i)	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) # sequence :: Monad m => Array i (m a) -> m (Array i a) #
Traversable (Proxy :: * -> *)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Traversable (NumMap k)
Instance details Defined in Data.Comp.Mapping Methods traverse :: Applicative f => (a -> f b) -> NumMap k a -> f (NumMap k b) # sequenceA :: Applicative f => NumMap k (f a) -> f (NumMap k a) # mapM :: Monad m => (a -> m b) -> NumMap k a -> m (NumMap k b) # sequence :: Monad m => NumMap k (m a) -> m (NumMap k a) #
Traversable (Map k)
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
Traversable f => Traversable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods traverse :: Applicative f0 => (a -> f0 b) -> ListT f a -> f0 (ListT f b) # sequenceA :: Applicative f0 => ListT f (f0 a) -> f0 (ListT f a) # mapM :: Monad m => (a -> m b) -> ListT f a -> m (ListT f b) # sequence :: Monad m => ListT f (m a) -> m (ListT f a) #
Traversable f => Traversable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b) # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a) # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) # sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #
Traversable (HashMap k)
Instance details Defined in Data.HashMap.Base Methods traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) # sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) # mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) # sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #
Traversable f => Traversable (Rec1 f)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #
Traversable (URec Char :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) # sequence :: Monad m => URec Char (m a) -> m (URec Char a) #
Traversable (URec Double :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Traversable (URec Float :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Traversable (URec Int :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Traversable (URec Word :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) # sequence :: Monad m => URec Word (m a) -> m (URec Word a) #
Traversable (URec (Ptr ()) :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b) # sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a) # mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b) # sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a) #
Traversable (Const m :: * -> *)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Traversable f => Traversable (Cxt h f)
Instance details Defined in Data.Comp.Term Methods traverse :: Applicative f0 => (a -> f0 b) -> Cxt h f a -> f0 (Cxt h f b) # sequenceA :: Applicative f0 => Cxt h f (f0 a) -> f0 (Cxt h f a) # mapM :: Monad m => (a -> m b) -> Cxt h f a -> m (Cxt h f b) # sequence :: Monad m => Cxt h f (m a) -> m (Cxt h f a) #
Traversable f => Traversable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) #
Traversable f => Traversable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b) # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a) # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) # sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) #
Traversable f => Traversable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable (K1 i c :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #
(Traversable f, Traversable g) => Traversable (f :+: g)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Traversable f, Traversable g) => Traversable (f :*: g)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
(Traversable f, Traversable g) => Traversable (f :+: g)
Instance details Defined in Data.Comp.Ops Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Traversable f, Traversable g) => Traversable (f :*: g)
Instance details Defined in Data.Comp.Ops Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
Traversable f => Traversable (f :&: a)
Instance details Defined in Data.Comp.Ops Methods traverse :: Applicative f0 => (a0 -> f0 b) -> (f :&: a) a0 -> f0 ((f :&: a) b) # sequenceA :: Applicative f0 => (f :&: a) (f0 a0) -> f0 ((f :&: a) a0) # mapM :: Monad m => (a0 -> m b) -> (f :&: a) a0 -> m ((f :&: a) b) # sequence :: Monad m => (f :&: a) (m a0) -> m ((f :&: a) a0) #
Traversable f => Traversable (M1 i c f)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
(Traversable f, Traversable g) => Traversable (f :.: g)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #

pr :: p :< q => q a -> p a #

This function projects the component of type e out or the compound value of type p.

type (:<) (f :: * -> *) (g :: * -> *) = Proj (ComprEmb (Elem f g)) f g infixl 5 #

The constraint e :< p expresses that e is a component of the type p. That is, p is formed by binary products using the type e. The occurrence of e must be unique. For example we have Int :< (Bool,(Int,Bool)) but not Bool :< (Bool,(Int,Bool)).

fsnd :: (f :*: g) a -> g a #

ffst :: (f :*: g) a -> f a #

data ((f :: k -> *) :*: (g :: k -> *)) (a :: k) :: forall k. (k -> *) -> (k -> *) -> k -> * infixr 8 #

Formal product of signatures (functors).

Constructors

(f a) :*: (g a) infixr 8

Instances

Proj (Found p) f g => Proj (Found (Ri p)) f (g' :*: g)
Instance details Defined in Data.Comp.Multi.Projection Methods pr' :: Proxy (Found (Ri p)) -> (g' :*: g) a -> f a
Proj (Found p) f g => Proj (Found (Le p)) f (g :*: g')
Instance details Defined in Data.Comp.Multi.Projection Methods pr' :: Proxy (Found (Le p)) -> (g :*: g') a -> f a
(Proj (Found p1) f1 g, Proj (Found p2) f2 g) => Proj (Found (Sum p1 p2)) (f1 :*: f2) g
Instance details Defined in Data.Comp.Multi.Projection Methods pr' :: Proxy (Found (Sum p1 p2)) -> g a -> (f1 :*: f2) a
(Functor f, Functor g) => Functor (f :*: g)
Instance details Defined in Data.Comp.Ops Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b # (<$) :: a -> (f :: g) b -> (f :: g) a #
(Foldable f, Foldable g) => Foldable (f :*: g)
Instance details Defined in Data.Comp.Ops Methods fold :: Monoid m => (f :: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :: g) a -> b # foldr1 :: (a -> a -> a) -> (f :: g) a -> a # foldl1 :: (a -> a -> a) -> (f :: g) a -> a # toList :: (f :: g) a -> [a] # null :: (f :: g) a -> Bool # length :: (f :: g) a -> Int # elem :: Eq a => a -> (f :: g) a -> Bool # maximum :: Ord a => (f :: g) a -> a # minimum :: Ord a => (f :: g) a -> a # sum :: Num a => (f :: g) a -> a # product :: Num a => (f :: g) a -> a #
(Traversable f, Traversable g) => Traversable (f :*: g)
Instance details Defined in Data.Comp.Ops Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #

lookupNumMap' :: Int -> NumMap t a -> Maybe a #

lookupNumMap :: a -> Int -> NumMap t a -> a #

prodMap :: Mapping m k => v1 -> v2 -> m v1 -> m v2 -> m (v1, v2) #

This function constructs the pointwise product of two maps each with a default value.

number :: Traversable f => f a -> f (Numbered a) #

This function numbers the components of the given functorial value with consecutive integers starting at 0.

unNumbered :: Numbered a -> a #

data Numbered a #

This type is used for numbering components of a functorial value.

Constructors

Numbered Int a

Instances

Mapping (NumMap k) (Numbered k)
Instance details Defined in Data.Comp.Mapping Methods (&) :: NumMap k v -> NumMap k v -> NumMap k v # (\|->) :: Numbered k -> v -> NumMap k v # empty :: NumMap k v # prodMapWith :: (v1 -> v2 -> v) -> v1 -> v2 -> NumMap k v1 -> NumMap k v2 -> NumMap k v # findWithDefault :: a -> Numbered k -> NumMap k a -> a #

class Functor m => Mapping (m :: * -> *) k | m -> k where #

Minimal complete definition

(&), (|->), empty, prodMapWith, findWithDefault

Methods

(&) :: m v -> m v -> m v infixr 0 #

left-biased union of two mappings.

(|->) :: k -> v -> m v infix 1 #

This operator constructs a singleton mapping.

empty :: m v #

This is the empty mapping.

prodMapWith :: (v1 -> v2 -> v) -> v1 -> v2 -> m v1 -> m v2 -> m v #

This function constructs the pointwise product of two maps each with a default value.

findWithDefault :: a -> k -> m a -> a #

Returns the value at the given key or returns the given default when the key is not an element of the map.

Instances

Mapping (NumMap k) (Numbered k)
Instance details Defined in Data.Comp.Mapping Methods (&) :: NumMap k v -> NumMap k v -> NumMap k v # (\|->) :: Numbered k -> v -> NumMap k v # empty :: NumMap k v # prodMapWith :: (v1 -> v2 -> v) -> v1 -> v2 -> NumMap k v1 -> NumMap k v2 -> NumMap k v # findWithDefault :: a -> Numbered k -> NumMap k a -> a #

data NumMap k v #

Instances

Functor (NumMap k)
Instance details Defined in Data.Comp.Mapping Methods fmap :: (a -> b) -> NumMap k a -> NumMap k b # (<$) :: a -> NumMap k b -> NumMap k a #
Foldable (NumMap k)
Instance details Defined in Data.Comp.Mapping Methods fold :: Monoid m => NumMap k m -> m # foldMap :: Monoid m => (a -> m) -> NumMap k a -> m # foldr :: (a -> b -> b) -> b -> NumMap k a -> b # foldr' :: (a -> b -> b) -> b -> NumMap k a -> b # foldl :: (b -> a -> b) -> b -> NumMap k a -> b # foldl' :: (b -> a -> b) -> b -> NumMap k a -> b # foldr1 :: (a -> a -> a) -> NumMap k a -> a # foldl1 :: (a -> a -> a) -> NumMap k a -> a # toList :: NumMap k a -> [a] # null :: NumMap k a -> Bool # length :: NumMap k a -> Int # elem :: Eq a => a -> NumMap k a -> Bool # maximum :: Ord a => NumMap k a -> a # minimum :: Ord a => NumMap k a -> a # sum :: Num a => NumMap k a -> a # product :: Num a => NumMap k a -> a #
Traversable (NumMap k)
Instance details Defined in Data.Comp.Mapping Methods traverse :: Applicative f => (a -> f b) -> NumMap k a -> f (NumMap k b) # sequenceA :: Applicative f => NumMap k (f a) -> f (NumMap k a) # mapM :: Monad m => (a -> m b) -> NumMap k a -> m (NumMap k b) # sequence :: Monad m => NumMap k (m a) -> m (NumMap k a) #
Mapping (NumMap k) (Numbered k)
Instance details Defined in Data.Comp.Mapping Methods (&) :: NumMap k v -> NumMap k v -> NumMap k v # (\|->) :: Numbered k -> v -> NumMap k v # empty :: NumMap k v # prodMapWith :: (v1 -> v2 -> v) -> v1 -> v2 -> NumMap k v1 -> NumMap k v2 -> NumMap k v # findWithDefault :: a -> Numbered k -> NumMap k a -> a #

type Inh f p q g = q :< p => Inh' f p q g Source #

The type of semantic functions for inherited attributes.

type Inh' f p q g = forall m i a. (Mapping m i, ?below :: i -> p a, ?above :: p a) => f i -> m (q (Context g a)) Source #

The type of semantic functions for inherited attributes. For defining semantic functions use the type Inh, which includes the inherited attribute that is defined by the semantic function into the available attributes.

type Syn f p q g = q :< p => Syn' f p q g Source #

The type of semantic functions for synthesised attributes.

type Syn' f p q g = forall child a. (?below :: child -> p a, ?above :: p a) => f child -> q (Context g a) Source #

The type of semantic functions for synthesised attributes. For defining semantic functions use the type Syn, which includes the synthesised attribute that is defined by the semantic function into the available attributes.

below :: (?below :: child -> q a, p :< q) => child -> p a Source #

This function provides access to attributes of the immediate children of the current node.

above :: (?above :: q a, p :< q) => p a Source #

This function provides access to attributes of the current node

prodSyn :: (p :< c, q :< c) => Syn f c p g -> Syn f c q g -> Syn f c (p :*: q) g Source #

Combines the semantic functions for two synthesised attributes to form a semantic function for the compound attribute consisting of the two original attributes.

(|*|) :: (p :< c, q :< c) => Syn f c p g -> Syn f c q g -> Syn f c (p :*: q) g Source #

Combines the semantic functions for two synthesised attributes to form a semantic function for the compound attribute consisting of the two original attributes.

prodInh :: (p :< c, q :< c, Functor p, Functor q) => Inh f c p g -> Inh f c q g -> Inh f c (p :*: q) g Source #

Combines the semantic functions for two inherited attributes to form a semantic function for the compound attribute consisting of the two original attributes.

(>*<) :: (p :< c, q :< c, Functor p, Functor q) => Inh f c p g -> Inh f c q g -> Inh f c (p :*: q) g Source #

Combines the semantic functions for two inherited attributes to form a semantic function for the compound attribute consisting of the two original attributes.